<html>
<head>
<title>APEX Tool</title>
<script language="javascript"> 
function toggle() {
	var ele = document.getElementById("toggleText");
	var text = document.getElementById("displayText");
	if(ele.style.display == "block") {
    		ele.style.display = "none";
		text.innerHTML = "Abstract";
  	}
	else {
		ele.style.display = "block";
		text.innerHTML = "hide";
	}
} 
</script>
</head>
<body>
<img src="Apexlogo.png" alt="APEX logo" align="left" height="100px" width="100px"/><h1><em><center><font color="blue">APEX</font><center></em></h1>
<table align="right">
<tr>
<td><input type="text"/><input type="submit" value="Search"/></td>
</tr>
</table><br/><br/><br/>
<hr size="2"/>
<center><a href="APEX.html">Home</a>  |  <a href="APEXAbout.html">About</a>  |  <a href="DownloadsAPEX.html">Downloads</a>  |  <a href="DocumentationAPEX.html">Documentation</a>  |  <a href="pubsAPEX.html">Publications</a>  |  <a href="editAPEX.html">Online Editor</a>  |  <a href="CaseStudyAPEX.html">Case Studies</a>  |  <a href="SupportAPEX.html">Support Page</a></center>
<hr size="2"/><br/> 
<center>Publications</center>
<input type="button" value="Abstract" id="displayText" onclick="javascript:toggle();"/>
<div id="toggleText" style="display: none"><h1>
<table border="3">
<tr>
<td>
In this paper, we propose a new randomised algorithm for  
deciding language equivalence for probabilistic automata. This algorithm  
is based on polynomial identity testing and thus returns an answer with  
an error probability that can be made arbitrarily small. We implemented  
our algorithm, as well as deterministic algorithms of Tzeng and Doyen  
et al., optimised for running time whilst adequately handling issues of  
numerical stability. We conducted extensive benchmarking experiments,  
including the verification of randomised anonymity protocols, the out-  
come of which establishes that the randomised algorithm significantly  
outperforms the deterministic ones in a majority of our test cases.  
Finally, we also provide fine-grained analytical bounds on the complexity  
of these algorithms, accounting for the differences in performance.
</td>
</tr>
</table>  